add numerical recipes library

lib/nr/cpp/recipes/tred2.cpp

@@ -0,0 +1,73 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::tred2(Mat_IO_DP &a, Vec_O_DP &d, Vec_O_DP &e)
+{
+	int l,k,j,i;
+	DP scale,hh,h,g,f;
+
+	int n=d.size();
+	for (i=n-1;i>0;i--) {
+		l=i-1;
+		h=scale=0.0;
+		if (l > 0) {
+			for (k=0;k<l+1;k++)
+				scale += fabs(a[i][k]);
+			if (scale == 0.0)
+				e[i]=a[i][l];
+			else {
+				for (k=0;k<l+1;k++) {
+					a[i][k] /= scale;
+					h += a[i][k]*a[i][k];
+				}
+				f=a[i][l];
+				g=(f >= 0.0 ? -sqrt(h) : sqrt(h));
+				e[i]=scale*g;
+				h -= f*g;
+				a[i][l]=f-g;
+				f=0.0;
+				for (j=0;j<l+1;j++) {
+				// Next statement can be omitted if eigenvectors not wanted
+					a[j][i]=a[i][j]/h;
+					g=0.0;
+					for (k=0;k<j+1;k++)
+						g += a[j][k]*a[i][k];
+					for (k=j+1;k<l+1;k++)
+						g += a[k][j]*a[i][k];
+					e[j]=g/h;
+					f += e[j]*a[i][j];
+				}
+				hh=f/(h+h);
+				for (j=0;j<l+1;j++) {
+					f=a[i][j];
+					e[j]=g=e[j]-hh*f;
+					for (k=0;k<j+1;k++)
+						a[j][k] -= (f*e[k]+g*a[i][k]);
+				}
+			}
+		} else
+			e[i]=a[i][l];
+		d[i]=h;
+	}
+	// Next statement can be omitted if eigenvectors not wanted
+	d[0]=0.0;
+	e[0]=0.0;
+	// Contents of this loop can be omitted if eigenvectors not
+	//	wanted except for statement d[i]=a[i][i];
+	for (i=0;i<n;i++) {
+		l=i;
+		if (d[i] != 0.0) {
+			for (j=0;j<l;j++) {
+				g=0.0;
+				for (k=0;k<l;k++)
+					g += a[i][k]*a[k][j];
+				for (k=0;k<l;k++)
+					a[k][j] -= g*a[k][i];
+			}
+		}
+		d[i]=a[i][i];
+		a[i][i]=1.0;
+		for (j=0;j<l;j++) a[j][i]=a[i][j]=0.0;
+	}
+}